# 2021 JMPSC Invitationals Problems/Problem 2

## Problem

Two quadrilaterals are drawn on the plane such that they share no sides. What is the maximum possible number of intersections of the boundaries of the two quadrilaterals?

## Solution

We find that it is possible to construct the maximal points, where each side of one quadrilateral intersects all four sides of the other quadrilateral.

~samrocksnature

## Solution 2

Take two concave quadrilaterals. Call two lines "somewhat parallel" if the different in their slopes is less than . An arrow has approximately lines which are "somewhat" parallel, which means arrows that are to each other form intersections. ~Geometry285

## Solution 3

A line can intersect other non-parallel lines times. If we draw quadrilaterals with non-parallel sides, it would then be possible to get intersections.

~Mathdreams

## See also

- Other 2021 JMPSC Invitationals Problems
- 2021 JMPSC Invitationals Answer Key
- All JMPSC Problems and Solutions

The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.